SPFirst-L07

SPFirst-L07 - Signal Processing First Lecture 7 Fourier Series& Spectrum EE-2025 Spring-2005 jMc 3 READING ASSIGNMENTS This Lecture Fourier

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Unformatted text preview: Signal Processing First Lecture 7 Fourier Series & Spectrum 9/13/2006 EE-2025 Spring-2005 jMc 3 READING ASSIGNMENTS ¡ This Lecture: ¡ Fourier Series in Ch 3, Sects 3 Fourier Series in Ch 3, Sects 3-4, 3 4, 3-5 & 3 5 & 3-6 ¡ Replaces pp. 62-66 in Ch 3 in DSP First ¡ Notation: a k for Fourier Series ¡ Other Reading: ¡ Next Lecture: Sampling 9/13/2006 EE-2025 Spring-2005 jMc 4 LECTURE OBJECTIVES ¡ ANALYSIS ANALYSIS via Fourier Series ¡ For PERIODIC signals: x(t+T ) = x(t) ¡ SPECTRUM SPECTRUM from Fourier Series ¡ a k is Complex Amplitude for k-th Harmonic ∫ − = ) / 2 ( 1 ) ( T dt e t x a t T k j T k π 9/13/2006 EE-2025 Spring-2005 jMc 5 100 250 –100 –250 f (in Hz) 3 / 7 π j e 3 / 7 π j e − 2 / 4 π j e − 2 / 4 π j e 10 SPECTRUM DIAGRAM ¡ Recall Complex Amplitude vs. Freq { } ∑ = − ∗ + + = N k t f j k t f j k k k e a e a a t x 1 2 2 ) ( π π k j k k e A a ϕ 2 1 = ∗ k a a 9/13/2006 EE-2025 Spring-2005 jMc 6 Harmonic Signal PERIOD/FREQUENCY of COMPLEX EXPONENTIAL: t f k j k k e a t x 2 ) ( π ∑ ∞ −∞ = = ( ) 1 or 2 2 f T T f = = = π ω π 9/13/2006 EE-2025 Spring-2005 jMc 7 Example ) 3 ( sin ) ( 3...
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This note was uploaded on 03/03/2010 for the course EE 48976 taught by Professor Nayak during the Spring '10 term at USC.

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SPFirst-L07 - Signal Processing First Lecture 7 Fourier Series& Spectrum EE-2025 Spring-2005 jMc 3 READING ASSIGNMENTS This Lecture Fourier

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